Matrix elements in the SU(1,1)⊗SO(6)limit of the proton-neutron symplectic model

The matrix elements along the reduction chain Sp(12,R)⊃SU(1,1)⊗SO(6)⊃U(1)⊗SUpn(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM)are considered.Closed analytical expressions are obtained for the matrix elements of the basic building blocks of the PNSM and the Sp(12,R)symplectic generators,allowing the computation of matrix elements of other physical operators as well.The computational technique developed in the present study generally provides us with the required algebraic tool for performing realistic symplectic-based shell-model calculations of nuclear collective excitations.Utilizing two simple examples,we illustrate the application of the theory.

Research on convergence of the nuclear matrix elements for 2νββ decays

In this work,the characteristics of 2νββ decays for six nuclei(36Ar,46Ca,48Ca,50Cr,70Zn,and 136Xe)in a mass range from A=36 to A=136 are studied within the nuclear shell model(NSM)framework.Calculations are presented for the half-lives,nuclear matrix elements(NMEs),phase space factors(G2ν),and convergence of the NMEs.The theoretical results agree well with the experimental data.In addition,we predict the half-lives of 2νββ decays for four nuclei.We focus on the convergence of the NMEs by analyzing the number of contributing intermediate 1+states(NC)for the nuclei of interest.We assume that NC is safely determined when the accumulated NMEs saturate 99.7%of the final calculated magnitude.From the calculations of the involved nuclei,we discover a connection between NC and the total number of intermediate 1+states(NT).According to the least squares fit,we conclude that the correlation is NC=(10.8±1.2)×N(0.29±0.02)T.

Non Degeneration of Fibonacci Series, Pascal’s Elements and Hex Series

Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.

Magic wavelengths for 6s_(1/2)→5d_(3/2,5/2)transitions of Yb~+ions

The wave functions,energy levels and matrix elements of Yb+ions are calculated using the relativistic configuration interaction plus core polarization(RCICP)method.The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined.Then,the magic wavelengths of the magnetic sublevel 6s_(1/2,m=1/2)→5d_(3/2,m=±3/2,±1/2)and 6s_(1/2,m=1/2)→5_(d5/2,m=±5/2,±3/2,±1/2)transitions in the linearly,right-handed,and left-handed polarized light are further determined.The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.

Variational Calculations for (ns2) 1Se, (np2) 1De and (nd2) 1Ge Resonance States for He Isoelectronic Sequences below the n = 2, 3 and 4 Hydrogenic Thresholds

This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed into three terms allowing to separate the kinetic energy, the electrons-nucleus interaction energy and the electron-electron interaction energy of the (2s2, 3s2 and 4s2) 1Se, (2p2, 3p2 and 4p2) 1De and (3d2 and 4d2) 1Ge resonance singlet states of the helium isoelectronic sequences. The states have been defined by using special forms of the Hylleraas type wave functions. The calculations have been carried out in the framework of the variational method using configuration interaction basis states with a real Hamiltonian. The agreement of the energy value of other states between the present theoretical values available in the literature is excellent. But as for the comparison of the kinetic energies, the electrons-nucleus energies interaction and the electron-electron interaction energies, we note a slight difference with the theoretical values common in literature.

Energy Positions of the ^1,3D^eRydberg Series of the He-Like Ions Up to the <i>N</i>= 9 Threshold

The doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the β-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (N = 2 - 9) in He-like ions up to Z = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.

Evidence for Non-existence of Oscillations in Photofield Emission Current in Gallium Arsenide

We have shown here the results of PFEC(photofield emission current)calculated for GaAs(gallium arsenide).We have used the initial state wavefunctions derived using the Kronig-Penney potential model for evaluating the PFEC.We have found that PFEC is not oscillatory as obtained by Modinos and Klient,[Solid State Commun.50,651(1984)],but it is an exponential function.

Stiffness Matrix Derivation of Space Beam Element at Elevated Temperature

<Abstract>Element stiffness equation is very important in structural analysis,and directly influences the accuracy of the results.At present,derivation method of element stiffness equation is relatively mature under ambient temperature,and the elastic phrase of material stress-strain curve is generally adopted as physical equation in derivation.However,the material stress-strain relationship is very complicated at elevated temperature,and its form is not unique,which brings great diffculty to the derivation of element stiffness equation.Referring to the derivation method of element stiffness equation at ambient temperature,by using the continuous function of stress-strain-temperature at elevated temperature,and based on the principle of virtual work,the stiffness equation of space beam element and the formulas of stiffness matrix are derived in this paper,which provide basis for finite element analysis on structures at elevated temperature.

First lattice QCD calculation of semileptonic decays of charmed-strange baryonsΞc

While the standard model is the most successful theory to describe all the interactions and constituents of elementary particle physics,it has been constantly scrutinized for over four decades.Weak decays of charm quarks can be used to measure the coupling strength between quarks in different families and serve as an ideal probe for CP violation.As the lowest charm-strange baryons with three different flavors,Ξ;baryons(composed of csu or csd)have been extensively studied in experiments.In this study,we use state-of-the-art lattice QCD techniques to generate 2+1 clover fermion ensembles with two lattice spacings,a=(0.108,0.080 fm).Then,we present the first ab-initio lattice QCD calculation of the Ξ;→Ξ form factors.Our theoretical results for the Ξc→Ξl;v;decay widths are consistent with and approximately two times more precise than the latest measurements by the ALICE and Belle collaborations.Based on the latest experimental measurements,we independently obtain the quark-mixing matrix element |V;|,which is in good agreement with results from other theoretical approaches.

Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

In this paper,the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles.For axially deformed nuclei,two different types of density profiles are used to describe their charge distributions.For the same charge distributions expanded with different basis functions,the corresponding longitudinal form factors are derived and compared with each other.Results show the multipoles C_λ of longitudinal form factors are independent of the basis functions of charge distributions.Further numerical calculations of longitudinal form factors of^(12)C indicates that the C_0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions.For deformed nuclei,their charge RMS radii can also be determined accurately by the C_0 measurement.The studies in this paper examine the model-independent properties of electron scattering,which are useful for interpreting electron scattering experiments on exotic deformed nuclei.

2νββ-decay to first 2^+states with partial isospin symmetry restoration from spherical QRPA calculations

Using partially restored isospin symmetry,we calculate the nuclear matrix elements for a special decay mode of a two-neutrino double beta decay–the decay to the first 2+excited states.Employing the realistic CD–Bonn nuclear force,we analyze the dependence of the nuclear matrix elements on the isovector and isoscalar parts of proton–neutron particle–particle interactions.The dependence on the different nuclear matrix elements is observed,and the results are explained.We also provide the phase space factors using numerical electron wavefunctions and properly chosen excitation energies.Finally,we present our results for the half-lives of this decay mode for different nuclei.